
Preprocessing Cost Relations
=====================================

#### Computed strongly connected components 
0. recursive  : [f1/27]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f4/17]
3. non_recursive  : [f1_loop_cont/18]
4. non_recursive  : [f3/17]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f1/27
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f1_loop_cont/18
4. SCC is partially evaluated into f3/17

Control-Flow Refinement of Cost Relations
=====================================

### Specialization of cost equations f1/27 
* CE 5 is refined into CE [8] 
* CE 4 is refined into CE [9] 
* CE 3 is refined into CE [10] 


### Cost equations --> "Loop" of f1/27 
* CEs [10] --> Loop 7 
* CEs [8] --> Loop 8 
* CEs [9] --> Loop 9 

### Ranking functions of CR f1(A,B,C,D,E,F,G,H,I,J,K,L,M,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1) 
* RF of phase [7]: [A-B,-B+H]

#### Partial ranking functions of CR f1(A,B,C,D,E,F,G,H,I,J,K,L,M,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1) 
* Partial RF of phase [7]:
  - RF of loop [7:1]:
    A-B
    -B+H


### Specialization of cost equations f1_loop_cont/18 
* CE 7 is refined into CE [11] 
* CE 6 is refined into CE [12] 


### Cost equations --> "Loop" of f1_loop_cont/18 
* CEs [11] --> Loop 10 
* CEs [12] --> Loop 11 

### Ranking functions of CR f1_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) 

#### Partial ranking functions of CR f1_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) 


### Specialization of cost equations f3/17 
* CE 1 is refined into CE [13] 
* CE 2 is refined into CE [14,15,16,17] 


### Cost equations --> "Loop" of f3/17 
* CEs [13,14,15,16,17] --> Loop 12 

### Ranking functions of CR f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,C1) 

#### Partial ranking functions of CR f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,C1) 


Computing Bounds
=====================================

#### Cost of chains of f1(A,B,C,D,E,F,G,H,I,J,K,L,M,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1):
* Chain [[7],9]: 1*it(7)+0
  Such that:it(7) =< -B+H

  with precondition: [C1=2,C=E,A=H,A=J1+1,B>=2,K1>=2,A>=B+1,E1>=K1] 

* Chain [[7],8]: 1*it(7)+0
  Such that:it(7) =< A-B

  with precondition: [C1=3,C=E,A=H,B>=2,A>=B+1] 

* Chain [9]: 0
  with precondition: [C1=2,A=B,E=C,I1=F,J1=G,A=H,E=P1,A>=2,K1>=2,E1>=K1] 

* Chain [8]: 0
  with precondition: [C1=3,H=A,E=C,B>=2,H>=B] 


#### Cost of chains of f1_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R):
* Chain [11]: 0
  with precondition: [A=2] 

* Chain [10]: 0
  with precondition: [A=3] 


#### Cost of chains of f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,C1):
* Chain [12]: 1*aux(1)+0
  with precondition: [] 


Closed-form bounds of f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,C1): 
-------------------------------------
* Chain [12] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,C1): inf 
Asymptotic class: infinity 
* Total analysis performed in 129 ms.

